Originally Posted by 2000grad
Kit means: "A set of articles or implements used for a specific purpose" or of this applies to clothing: "A collection of clothing and other personal effects"
Kit refers not just to the "uniform" but to all the "gear" a player may have eg the "uniform", the boots, shin guards, strappings, laces, etc.
Just like a shaving-kit or any other type of kit.
The "uniform" is correctly referred to as a "strip", which forms one part of a players kit.
In America sports, uniform means all of this, too.